Common, complex diseases together account for a large portion of the health care burden in the United States, and genetic analysis of these traits remains one of the major challenges facing biomedical researchers. Recent advances in high-throughput technologies have led to increasing availability of large-scale genetic sequence information and other related biological data sets. If robust, powerful statistical and computational methods and tools are developed to analyze these data, then progress can be made on identifying and characterizing the genetic components of complex disorders. This, in turn, has the potential to (1) lead to better understanding of the biology of such disorders, (2) clarify the role of environmental risk factors, which could be targets of cost-effective treatment and prevention strategies, and (3) lead to improvements in personalized medical care. Our goal is development of robust, powerful trait-association data analysis methods that will be useful for a wide variety of genetic and other omics predictors in a full spectrum of study designs, ranging from unrelated samples with population structure to individuals sampled from a complex, inbred pedigree. Specifically, we propose development of novel methods for binary, quantitative, and longitudinal trait mapping with a range of predictors, such as genotype, genomic sequence, transcriptome, expression, metabolomic, methylation, proteomic or other data, where these methods incorporate relevant covariates and account for population structure and/or relatedness of individuals in the sample.